On the optimal control of the steel annealing processes as a two-stage hybrid systems via different versions of PSO algorithms

The computation of optimal control variables for a two-stage steel annealing process (SAP) which comprises of one or more furnaces is proposed in this paper. The heating and soaking furnaces of the steel annealing line form two-stage hybrid systems. Three algorithms including particle swarm optimization (PSO) with globally and locally tuned parameters (GLbest PSO), a parameter free PSO algorithm (pf-PSO), and a PSO like algorithm via extrapolation (ePSO) are considered to solve this optimal control problem for the two-stage steel annealing processes (SAP). The optimal solutions including optimal line speed, optimal cost, and job completion time obtained through these three methods are compared with each other and those obtained via conventional PSO (cPSO) with time varying inertia weight (TVIW) and time varying acceleration coefficient (TVAC). From the results obtained through the four algorithms considered, the efficacy and validity of each algorithm are analyzed.